Interactive Real Analysis5.1. Open and Closed Sets
Definition 5.1.1: Open and Closed Sets
A set
U 
R
is called open, if for each
x 
U
there exists an
> 0
such that the interval
( x - ,
x + )
is contained in U. Such an interval is often called an
-neighborhood of x,
or simply a neighborhood of x.
Context
R
is called open, if for each
x U
there exists an
> 0
such that the interval
( x - ,
x + )
is contained in U. Such an interval is often called an
-neighborhood of x,
or simply a neighborhood of x.
A set F is called closed if the complement of F, R \ F, is open.
Context